The concept of orthogonality has been broadly generalized in mathematics, as well as in areas such as chemistry, and engineering. The word comes from the Greek ὀρθός, meaning upright, and γωνία, the ancient Greek ὀρθογώνιον orthogōnion and classical Latin orthogonium originally denoted a rectangle. Later, they came to mean a right triangle, in the 12th century, the post-classical Latin word orthogonalis came to mean a right angle or something related to a right angle. In geometry, two Euclidean vectors are orthogonal if they are perpendicular, i. e. they form a right angle, two vectors, x and y, in an inner product space, V, are orthogonal if their inner product ⟨ x, y ⟩ is zero. This relationship is denoted x ⊥ y, two vector subspaces, A and B, of an inner product space, V, are called orthogonal subspaces if each vector in A is orthogonal to each vector in B. The largest subspace of V that is orthogonal to a subspace is its orthogonal complement. Given a module M and its dual M∗, an e
The line segments AB and CD are orthogonal to each other.
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The term laser originated as an acronym for light amplification by stimulated emission of radiation, the first laser was built in 1960 by Theodore H. Maiman at Hughes Research Laboratories, based on theoretical work by Charles Hard Townes and Arthur Leonard Schawlow. A laser differs from other sources of light in that it emits light coherently, spatial coherence allows a laser to be focused to a tight spot, enabling applications such as laser cutting and lithography. Spatial coherence also allows a laser beam to stay narrow over great distances, Lasers can also have high temporal coherence, which allows them to emit light with a very narrow spectrum, i. e. they can emit a single color of light. Temporal coherence can be used to produce pulses of light as short as a femtosecond, Lasers are distinguished from other light sources by their coherence
Red (660 & 635 nm), green (532 & 520 nm) and blue-violet (445 & 405 nm) lasers
Laser beams in fog, reflected on a car windshield
This is different from other light-reflecting objects that do not preserve much of the original wave signal other than color and diffuse reflected light. The most familiar type of mirror is the mirror, which has a flat screen surface. Curved mirrors are used, to produce magnified or diminished images or focus light or simply distort the reflected image. Mirrors are commonly used for personal grooming or admiring oneself, decoration, Mirrors are also used in scientific apparatus such as telescopes and lasers, cameras, and industrial machinery. Most mirrors are designed for light, however, mirrors designed for other wavelengths of electromagnetic radiation are also used. The first mirrors used by people were most likely pools of dark, still water, the requirements for making a good mirror are a surface with a very high degree of flatness, and a surface roughness smaller than the wavelength of the light. The earliest manufactured mirrors were pieces of polished stone such as obsidian, exa
A mirror, reflecting a vase
A first surface mirror
coated with aluminum and enhanced with dielectric
coatings. The angle of the incident light (represented by both the light in the mirror and the shadow behind it) exactly matches the angle of reflection (the reflected light shining on the table).
A sculpture of a lady looking into a mirror, India
Light is electromagnetic radiation within a certain portion of the electromagnetic spectrum. The word usually refers to light, which is visible to the human eye and is responsible for the sense of sight. Visible light is defined as having wavelengths in the range of 400–700 nanometres, or 4.00 × 10−7 to 7.00 × 10−7 m. This wavelength means a range of roughly 430–750 terahertz. The main source of light on Earth is the Sun, sunlight provides the energy that green plants use to create sugars mostly in the form of starches, which release energy into the living things that digest them. This process of photosynthesis provides virtually all the used by living things. Historically, another important source of light for humans has been fire, with the development of electric lights and power systems, electric lighting has effectively replaced firelight. Some species of animals generate their own light, a process called bioluminescence, for example, fireflies use light to locate mates, and vampir
An example of refraction of light. The straw appears bent, because of refraction of light as it enters liquid from air.
A triangular prism dispersing a beam of white light. The longer wavelengths (red) and the shorter wavelengths (blue) get separated.